Question

1. the sum of the angle measures of a triangle is 180°. find the value of x. then find the angle measures of the triangle.

Explanation:

Step1: Set up the equation

The sum of angles in a triangle is 180°. So, $x + 2x+(x + 20)=180$.

Step2: Combine like - terms

Combine the $x$ terms on the left - hand side: $(x + 2x+x)+20 = 180$, which simplifies to $4x+20 = 180$.

Step3: Isolate the variable term

Subtract 20 from both sides of the equation: $4x+20 - 20=180 - 20$, resulting in $4x = 160$.

Step4: Solve for $x$

Divide both sides by 4: $\frac{4x}{4}=\frac{160}{4}$, so $x = 40$.

Step5: Find the angle measures

The first angle is $x=40^{\circ}$.
The second angle is $2x = 2\times40 = 80^{\circ}$.
The third angle is $x + 20=40+20 = 60^{\circ}$.

Answer:

$x = 40$, the angle measures are $40^{\circ},80^{\circ},60^{\circ}$